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Extensions 1→N→G→Q→1 with N=C4 and Q=C4○D20

Direct product G=N×Q with N=C4 and Q=C4○D20
dρLabelID
C4×C4○D20160C4xC4oD20320,1146

Semidirect products G=N:Q with N=C4 and Q=C4○D20
extensionφ:Q→Aut NdρLabelID
C4⋊1(C4○D20) = Dic10⋊24D4φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4:1(C4oD20)320,1225
C4⋊2(C4○D20) = C42.228D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4:2(C4oD20)320,1220
C4⋊3(C4○D20) = D20⋊24D4φ: C4○D20/D20 → C2 ⊆ Aut C4160C4:3(C4oD20)320,1223
C4⋊4(C4○D20) = C10.2- 1+4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4:4(C4oD20)320,1179
C4⋊5(C4○D20) = C42.276D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4:5(C4oD20)320,1149

Non-split extensions G=N.Q with N=C4 and Q=C4○D20
extensionφ:Q→Aut NdρLabelID
C4.1(C4○D20) = Dic10⋊2D4φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.1(C4oD20)320,389
C4.2(C4○D20) = Dic10.D4φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.2(C4oD20)320,394
C4.3(C4○D20) = D20⋊3D4φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.3(C4oD20)320,413
C4.4(C4○D20) = D20.D4φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.4(C4oD20)320,414
C4.5(C4○D20) = Dic5⋊Q16φ: C4○D20/Dic10 → C2 ⊆ Aut C4320C4.5(C4oD20)320,420
C4.6(C4○D20) = Dic10.11D4φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.6(C4oD20)320,425
C4.7(C4○D20) = Dic5⋊SD16φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.7(C4oD20)320,445
C4.8(C4○D20) = D20.12D4φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.8(C4oD20)320,446
C4.9(C4○D20) = C20⋊7D8φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.9(C4oD20)320,642
C4.10(C4○D20) = D4.1D20φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.10(C4oD20)320,643
C4.11(C4○D20) = D4.2D20φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.11(C4oD20)320,646
C4.12(C4○D20) = Q8⋊D20φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.12(C4oD20)320,654
C4.13(C4○D20) = Q8.1D20φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.13(C4oD20)320,655
C4.14(C4○D20) = C20⋊7Q16φ: C4○D20/Dic10 → C2 ⊆ Aut C4320C4.14(C4oD20)320,658
C4.15(C4○D20) = C42.106D10φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.15(C4oD20)320,1214
C4.16(C4○D20) = C42.114D10φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.16(C4oD20)320,1231
C4.17(C4○D20) = Dic10⋊10Q8φ: C4○D20/Dic10 → C2 ⊆ Aut C4320C4.17(C4oD20)320,1239
C4.18(C4○D20) = C42.122D10φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.18(C4oD20)320,1240
C4.19(C4○D20) = C42.136D10φ: C4○D20/Dic10 → C2 ⊆ Aut C4160C4.19(C4oD20)320,1257
C4.20(C4○D20) = Dic5.5D8φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.20(C4oD20)320,387
C4.21(C4○D20) = C4⋊C4.D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.21(C4oD20)320,391
C4.22(C4○D20) = C20⋊Q8⋊C2φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.22(C4oD20)320,392
C4.23(C4○D20) = (C8×Dic5)⋊C2φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.23(C4oD20)320,395
C4.24(C4○D20) = D10⋊D8φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.24(C4oD20)320,402
C4.25(C4○D20) = D10⋊SD16φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.25(C4oD20)320,405
C4.26(C4○D20) = C5⋊2C8⋊D4φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.26(C4oD20)320,407
C4.27(C4○D20) = C5⋊(C8⋊2D4)φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.27(C4oD20)320,409
C4.28(C4○D20) = Dic5.3Q16φ: C4○D20/C4×D5 → C2 ⊆ Aut C4320C4.28(C4oD20)320,419
C4.29(C4○D20) = Q8⋊C4⋊D5φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.29(C4oD20)320,422
C4.30(C4○D20) = C40⋊8C4.C2φ: C4○D20/C4×D5 → C2 ⊆ Aut C4320C4.30(C4oD20)320,424
C4.31(C4○D20) = Q8⋊Dic5⋊C2φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.31(C4oD20)320,427
C4.32(C4○D20) = D10⋊2SD16φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.32(C4oD20)320,434
C4.33(C4○D20) = C5⋊(C8⋊D4)φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.33(C4oD20)320,439
C4.34(C4○D20) = D10⋊Q16φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.34(C4oD20)320,440
C4.35(C4○D20) = C5⋊2C8.D4φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.35(C4oD20)320,443
C4.36(C4○D20) = C4×D4⋊D5φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.36(C4oD20)320,640
C4.37(C4○D20) = C42.48D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.37(C4oD20)320,641
C4.38(C4○D20) = C4×D4.D5φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.38(C4oD20)320,644
C4.39(C4○D20) = C42.51D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.39(C4oD20)320,645
C4.40(C4○D20) = C4×Q8⋊D5φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.40(C4oD20)320,652
C4.41(C4○D20) = C42.56D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.41(C4oD20)320,653
C4.42(C4○D20) = C4×C5⋊Q16φ: C4○D20/C4×D5 → C2 ⊆ Aut C4320C4.42(C4oD20)320,656
C4.43(C4○D20) = C42.59D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4320C4.43(C4oD20)320,657
C4.44(C4○D20) = C42.229D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.44(C4oD20)320,1229
C4.45(C4○D20) = C42.115D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.45(C4oD20)320,1233
C4.46(C4○D20) = C42.116D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.46(C4oD20)320,1234
C4.47(C4○D20) = C42.232D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.47(C4oD20)320,1250
C4.48(C4○D20) = C42.131D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.48(C4oD20)320,1252
C4.49(C4○D20) = C42.133D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.49(C4oD20)320,1254
C4.50(C4○D20) = C42.134D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C4160C4.50(C4oD20)320,1255
C4.51(C4○D20) = D10.12D8φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.51(C4oD20)320,401
C4.52(C4○D20) = D10.16SD16φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.52(C4oD20)320,404
C4.53(C4○D20) = C40⋊6C4⋊C2φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.53(C4oD20)320,406
C4.54(C4○D20) = C40⋊5C4⋊C2φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.54(C4oD20)320,411
C4.55(C4○D20) = D10.11SD16φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.55(C4oD20)320,432
C4.56(C4○D20) = D10.7Q16φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.56(C4oD20)320,436
C4.57(C4○D20) = (C2×C8).D10φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.57(C4oD20)320,441
C4.58(C4○D20) = D10⋊1C8.C2φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.58(C4oD20)320,442
C4.59(C4○D20) = C20.50D8φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.59(C4oD20)320,634
C4.60(C4○D20) = C20.38SD16φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.60(C4oD20)320,635
C4.61(C4○D20) = D4.3Dic10φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.61(C4oD20)320,636
C4.62(C4○D20) = C20.48SD16φ: C4○D20/D20 → C2 ⊆ Aut C4320C4.62(C4oD20)320,647
C4.63(C4○D20) = C20.23Q16φ: C4○D20/D20 → C2 ⊆ Aut C4320C4.63(C4oD20)320,648
C4.64(C4○D20) = Q8.3Dic10φ: C4○D20/D20 → C2 ⊆ Aut C4320C4.64(C4oD20)320,649
C4.65(C4○D20) = C42.113D10φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.65(C4oD20)320,1230
C4.66(C4○D20) = C42.117D10φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.66(C4oD20)320,1235
C4.67(C4○D20) = D20⋊10Q8φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.67(C4oD20)320,1251
C4.68(C4○D20) = C42.132D10φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.68(C4oD20)320,1253
C4.69(C4○D20) = C42.135D10φ: C4○D20/D20 → C2 ⊆ Aut C4160C4.69(C4oD20)320,1256
C4.70(C4○D20) = Dic10⋊Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4320C4.70(C4oD20)320,481
C4.71(C4○D20) = Dic10.Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4320C4.71(C4oD20)320,484
C4.72(C4○D20) = D10.12SD16φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.72(C4oD20)320,489
C4.73(C4○D20) = D10.17SD16φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.73(C4oD20)320,490
C4.74(C4○D20) = C4.Q8⋊D5φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.74(C4oD20)320,493
C4.75(C4○D20) = C20.(C4○D4)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.75(C4oD20)320,494
C4.76(C4○D20) = D20⋊Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.76(C4oD20)320,497
C4.77(C4○D20) = D20.Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.77(C4oD20)320,498
C4.78(C4○D20) = Dic10⋊2Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4320C4.78(C4oD20)320,502
C4.79(C4○D20) = Dic10.2Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4320C4.79(C4oD20)320,504
C4.80(C4○D20) = D10.13D8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.80(C4oD20)320,509
C4.81(C4○D20) = D10.8Q16φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.81(C4oD20)320,511
C4.82(C4○D20) = C2.D8⋊D5φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.82(C4oD20)320,512
C4.83(C4○D20) = C2.D8⋊7D5φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.83(C4oD20)320,515
C4.84(C4○D20) = D20⋊2Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.84(C4oD20)320,517
C4.85(C4○D20) = D20.2Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.85(C4oD20)320,518
C4.86(C4○D20) = (C2×C10).40D8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.86(C4oD20)320,594
C4.87(C4○D20) = C4⋊C4.228D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.87(C4oD20)320,595
C4.88(C4○D20) = C4⋊C4.230D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.88(C4oD20)320,597
C4.89(C4○D20) = C4⋊C4.231D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.89(C4oD20)320,598
C4.90(C4○D20) = C4⋊C4.233D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.90(C4oD20)320,623
C4.91(C4○D20) = C4⋊C4.236D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.91(C4oD20)320,630
C4.92(C4○D20) = C10.102+ 1+4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.92(C4oD20)320,1183
C4.93(C4○D20) = C10.52- 1+4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.93(C4oD20)320,1185
C4.94(C4○D20) = C10.112+ 1+4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.94(C4oD20)320,1186
C4.95(C4○D20) = C42.94D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.95(C4oD20)320,1201
C4.96(C4○D20) = C42.95D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.96(C4oD20)320,1202
C4.97(C4○D20) = C42.97D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.97(C4oD20)320,1204
C4.98(C4○D20) = C42.98D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C4160C4.98(C4oD20)320,1205
C4.99(C4○D20) = C20.14Q16φ: C4○D20/C2×C20 → C2 ⊆ Aut C4320C4.99(C4oD20)320,308
C4.100(C4○D20) = C4×C40⋊C2φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.100(C4oD20)320,318
C4.101(C4○D20) = C4×D40φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.101(C4oD20)320,319
C4.102(C4○D20) = C4.5D40φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.102(C4oD20)320,321
C4.103(C4○D20) = C42.264D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.103(C4oD20)320,324
C4.104(C4○D20) = C4×Dic20φ: C4○D20/C2×C20 → C2 ⊆ Aut C4320C4.104(C4oD20)320,325
C4.105(C4○D20) = C42.14D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4320C4.105(C4oD20)320,330
C4.106(C4○D20) = C42.16D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.106(C4oD20)320,337
C4.107(C4○D20) = D40⋊9C4φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.107(C4oD20)320,338
C4.108(C4○D20) = C42.19D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.108(C4oD20)320,340
C4.109(C4○D20) = C42.20D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.109(C4oD20)320,341
C4.110(C4○D20) = Dic20⋊9C4φ: C4○D20/C2×C20 → C2 ⊆ Aut C4320C4.110(C4oD20)320,343
C4.111(C4○D20) = C40⋊30D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.111(C4oD20)320,741
C4.112(C4○D20) = C40⋊29D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.112(C4oD20)320,742
C4.113(C4○D20) = C40.82D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.113(C4oD20)320,743
C4.114(C4○D20) = C40⋊2D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.114(C4oD20)320,761
C4.115(C4○D20) = C40⋊3D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.115(C4oD20)320,762
C4.116(C4○D20) = C40.4D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.116(C4oD20)320,764
C4.117(C4○D20) = C42.274D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.117(C4oD20)320,1142
C4.118(C4○D20) = C42.277D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.118(C4oD20)320,1151
C4.119(C4○D20) = C42.89D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.119(C4oD20)320,1190
C4.120(C4○D20) = C42.99D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.120(C4oD20)320,1206
C4.121(C4○D20) = C42.100D10φ: C4○D20/C2×C20 → C2 ⊆ Aut C4160C4.121(C4oD20)320,1207
C4.122(C4○D20) = C8×Dic10central extension (φ=1)320C4.122(C4oD20)320,305
C4.123(C4○D20) = C40⋊11Q8central extension (φ=1)320C4.123(C4oD20)320,306
C4.124(C4○D20) = C42.282D10central extension (φ=1)160C4.124(C4oD20)320,312
C4.125(C4○D20) = C8×D20central extension (φ=1)160C4.125(C4oD20)320,313
C4.126(C4○D20) = C8⋊6D20central extension (φ=1)160C4.126(C4oD20)320,315
C4.127(C4○D20) = C42.243D10central extension (φ=1)160C4.127(C4oD20)320,317
C4.128(C4○D20) = C40⋊Q8central extension (φ=1)320C4.128(C4oD20)320,328
C4.129(C4○D20) = C42.182D10central extension (φ=1)160C4.129(C4oD20)320,332
C4.130(C4○D20) = C8⋊9D20central extension (φ=1)160C4.130(C4oD20)320,333
C4.131(C4○D20) = C42.185D10central extension (φ=1)160C4.131(C4oD20)320,336
C4.132(C4○D20) = C42.6Dic5central extension (φ=1)160C4.132(C4oD20)320,552
C4.133(C4○D20) = C42.7Dic5central extension (φ=1)160C4.133(C4oD20)320,553
C4.134(C4○D20) = C42.187D10central extension (φ=1)160C4.134(C4oD20)320,627
C4.135(C4○D20) = C8×C5⋊D4central extension (φ=1)160C4.135(C4oD20)320,736
C4.136(C4○D20) = C40⋊32D4central extension (φ=1)160C4.136(C4oD20)320,738
C4.137(C4○D20) = C40⋊D4central extension (φ=1)160C4.137(C4oD20)320,754
C4.138(C4○D20) = C40⋊18D4central extension (φ=1)160C4.138(C4oD20)320,755
C4.139(C4○D20) = C42.93D10central extension (φ=1)160C4.139(C4oD20)320,1200

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